Thermodynamic properties of a relativistic Bose gas under rigid rotation

TL;DR

This paper investigates the thermodynamic behavior of a relativistic Bose gas under rotation, deriving key properties and identifying instabilities, supervorticity, and superluminal sound velocities at high temperatures and couplings.

Contribution

It provides a detailed analysis of the thermodynamics of a rotating relativistic Bose gas, including perturbative and nonperturbative effects, and explores stability and superfluid phenomena.

Findings

Identification of thermodynamic instabilities at high T and large $\Omega$ and $\alpha$.

Discovery of supervorticity where moment of inertia vanishes.

Observation of superluminal sound velocities under certain conditions.

Abstract

We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature ($T$), angular velocity ($\Omega$), and the coupling constant ($\alpha$). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain $T$ or $\alpha$. Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high $T$ and for large $\alpha$.